Masteries

Offense:
9

Defense:
0

Utility:
21

Pros:
Epic burst hero
Good chaser
Very good 1 vs 1
Creates chaos
Very much fun to play with

Cons:
Not the best farmer
They want to kill you first
Hard to master
Lacks CC in teamfight, can only kill one at the time

Pre-match:
You really want mid because she's very strong from the start already and it's not hard to handle. I don't suggest to go 1 vs 2 because they will kill your tower pretty fast, depends on their champs though.

Early game:
Start off with a Sapphire Crystal and 2 health potions for longer laning. When you are lvl 2 you can do much damage already, always try to use spell order: Q-W, so you silence him and do a little bonus damage. When you are lvl 4, try to use the spell order: Q-W-E, first damage, then you W to him which silence him and then E for slowing and eventually shackle him. Try to get that Catalyst the Protector fast so you can stay longer in the lane (when you lvl). And get boots for faster movement.

Mid game:
You are lvl 6 now. Try to finish your Rod of Ages, it needs some time. If you are doing well, buy a Mejai's Soulstealer, otherwise go Tear of the Goddess followed by Rylais Crystal Scepter.
When you want to attack an enemy I suggest you to do the following spellorder: E-Q-R-W. First slow him, then damage him, then use R for the silence and MORE damage, then go to him so he will get shackled and more damage and silence. If you see he's going to flee use: E-Q-W-R, so you can follow him better. Use ghost and ignite if you can't finish him with using all your spells. Another good spellorder: W-Q-E-R, The only thing is, Q is your most damagedealing spell, that's why I prefer to use R after Q. And there is a chance that you miss the enemy when you cast E.

Late game:
If you are doing well you have 5 items now, RoA, Mejais, Boots, Rylais and TotG. Finish your Archangel Staff and then go Zhonya's Ring. These last items are pretty expensive though, so there's a big chance you can't make it to them.
If you are not doing great you shouldn't have the Mejais, instead of that I suggest you a Banshees Veil, if they do very much physical damage, I suggest Randuin's Omen or Frozen Heart. Buy this item whenever you think it's necessarry.

Summoner spells:
Ghost and ignite are good for her, enemies can't flee and some extra damage can be useful. Some might pick flash to surprise the enemy, which can be very good.
Don't pick clarity, she's not very fast out of mana and it sucks late game.